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P, Q, and R are each rectangles. The length and width of rectangle P a
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05 Jan 2023, 00:37
05 Jan 2023, 00:37
2
Expert Reply
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Question Stats:
75% (02:00) correct
24% (02:19) wrong based on 62 sessions
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P, Q, and R are each rectangles. The length and width of rectangle P are 30 percent less and 20 percent greater, respectively than the length and width of rectangle R.
The length and width of rectangle Q are 40 percent greater and 40 percent less, respectively than the length and width of rectangle R.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
The length and width of rectangle Q are 40 percent greater and 40 percent less, respectively than the length and width of rectangle R.
Quantity A |
Quantity B |
The area of rectangle P |
The area of rectangle Q |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: P, Q, and R are each rectangles. The length and width of rectangle P a
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30 Jan 2023, 16:43
30 Jan 2023, 16:43
1
Expert Reply
OE
In this question you are asked to compare the area of rectangle P with that of rectangle Q. Since the information given is the relative size of the length and width of rectangles P and Q with respect to those of rectangle P, you should try to evaluate the relative areas using rectangle P's dimensions as the starting point.
If you assign x to the length of rectangle P, and y to its width, you get an area for rectangle P of xy. Because the length and width of rectangle P are 30 percent less and 20 percent greater, respectively than those of rectangle P, then the length and
width of rectangle P equal (1 - 0.3)* = o.yx and (l + o.2)y = i.2y. Thus, the area of rectangle P is (0.7*) (i.2y) = 0.84xy.
Similarly, the length and width of rectangle Q are 40 percent greater and 40 percent less, respectively, than those of rectangle P, so the length and width of rectangle Q equal (1 + 0.4)x = 1.4X and (1 - 0.4)y = 0.6y. Thus, the area of rectangle Q is (i.4x)(0.6y) = 0.84xy.
Thus, rectangles P and Q have equal area. Therefore, the two quantities are equal.
In this question you are asked to compare the area of rectangle P with that of rectangle Q. Since the information given is the relative size of the length and width of rectangles P and Q with respect to those of rectangle P, you should try to evaluate the relative areas using rectangle P's dimensions as the starting point.
If you assign x to the length of rectangle P, and y to its width, you get an area for rectangle P of xy. Because the length and width of rectangle P are 30 percent less and 20 percent greater, respectively than those of rectangle P, then the length and
width of rectangle P equal (1 - 0.3)* = o.yx and (l + o.2)y = i.2y. Thus, the area of rectangle P is (0.7*) (i.2y) = 0.84xy.
Similarly, the length and width of rectangle Q are 40 percent greater and 40 percent less, respectively, than those of rectangle P, so the length and width of rectangle Q equal (1 + 0.4)x = 1.4X and (1 - 0.4)y = 0.6y. Thus, the area of rectangle Q is (i.4x)(0.6y) = 0.84xy.
Thus, rectangles P and Q have equal area. Therefore, the two quantities are equal.
Re: P, Q, and R are each rectangles. The length and width of rectangle P a
[#permalink]
27 Feb 2023, 12:06
27 Feb 2023, 12:06
2
Quantity P : 0.7 L * 1.2 B = 0.84 LB
Quantity Q : 1.4L * 0.6 B = 0.84 LB , we take the unit 1 and reduce or increase as per question . if it is 30% more , it becomes 1.3 times the quantity however 30% less will make it 0.7 times the quantity. simple dollar equations , I add 30 cents to make 1 dollar 30 cents and take 30 cents to make it 70 cents .
Quantity Q : 1.4L * 0.6 B = 0.84 LB , we take the unit 1 and reduce or increase as per question . if it is 30% more , it becomes 1.3 times the quantity however 30% less will make it 0.7 times the quantity. simple dollar equations , I add 30 cents to make 1 dollar 30 cents and take 30 cents to make it 70 cents .
